Xi Jinping and Barack Obama should now plan a snorkelling trip to the Great Barrier Reef, guided by Kevin Rudd. Photographs: Jeff Hunter/Getty

Individuals make history. If the last leader of the Soviet Union had not been a man called Mikhail Gorbachev, the world would be a different place. So the character and views of China's leader-designate, Xi Jinping, who is currently visiting the United States, do matter. After spending several years failing to obtain a clear impression of President Hu, attention now turns to the man who will, barring accidents, succeed him.

The best thumbnail summary that I have read comes in a forthcoming book by Jonathan Fenby, titled Tiger Head, Snake Tails. (The title refers to modern China, not vice-president Xi.) As you would expect, the available evidence is thin and inconclusive. The fact that Xi suffered personally in the Cultural Revolution ("I ate a lot more bitterness than most people"), the reformist communist sympathies of his father, his evident pragmatism, the discovery that he has a sister in Canada, a brother in Hong Kong and a daughter studying under a pseudonym at Harvard: all this suggests someone who might push forward essential political reforms at home and be equipped with a better understanding of the west.

The fact that he has risen to the top by carefully staying on the right side of all the main groups in the communist establishment, his close ties to the People's Liberation Army, his remarkable outburst in Mexico in 2009, denouncing "some bored foreigners, with full stomachs, who have nothing better to do than point fingers at us": these straws point to a potentially colder wind from the east.

Every little phrase and gesture in his current American trip will be pored over with neo-Kremlinological zeal, to identify him as either great reformer or hardnosed realist. Or, inevitably, "enigmatic". As with Gorbachev, western leaders may get hints of the personality now, but we won't really know until he's firmly in the saddle, which means 2013 at the earliest.

Individuals make history, but they do not make it just as they please. Even when he becomes president, in spring 2013, Xi will face multiple constraints. China now seems to have a genuinely collective party leadership, more than the Soviet Union did. There are enormous economic and social tensions that have to be managed, from the country's own internal debt problem, through the rural-urban divide, to the difficulty of moving beyond an overwhelmingly export-led model of growth. There are the unresolved problems of Xinjiang and of Tibet, where an 18-year-old nun just burned herself to death in a despairing protest.

Increasingly, there is the voice of public opinion, using everything from street protests to micro-blogging sites such as Sina Weibo. That voice is often fiercely critical of official corruption and mismanagement, but it can also be very nationalist. And the truth is that there are now all the makings of a classic great power rivalry between China and the US, expressed most directly through a military buildup in the Pacific region. For all the obvious differences, the high seas rivalry between Britain and Germany 100 years ago should serve as a lesson in what to avoid.

So how should the west engage with China, and vice versa? Earlier this month, I saw two textbook examples of how not to do it – and one of how we should. At the Munich Security Conference, Zhang Zhijun, China's vice-minister of foreign affairs, woodenly waffled on about how "the people of Asia" had chosen a different path from the west, and how the west should simply leave China to go its own way. Oh, and by the way, there was no problem at all in the South China Sea, where everyone enjoys free navigation.

Sitting next to him, Senator John McCain launched into a ballistic attack. It is a matter of concern, he said, when a Vietnamese ship has its cables cut by a Chinese vessel. The Vietnamese remember 2,000 years of Chinese domination. People are immolating themselves in Tibet. The Arab spring represents universal aspirations and "the Arab spring is coming to China as well".

Part of me felt there was something magnificent about this – like John Wayne in the film True Grit, charging alone at four armed bandits, with the reins clenched between his teeth. But McCain's charge, like Wayne's, was so obviously done for the cameras and the audience back home.

Then there was a rare example of how to get it right. Kevin Rudd, Australia's foreign minister and a Mandarin-speaker, spoke briefly and pungently. People in Europe haven't fully woken up to what is happening, he said. China will have the world's largest economy within this decade. For the first time in 200 years the world's largest economy will be a non-democracy; for the first time in 500 years, it will be a non-western country.

Moreover, according to what Rudd called "credible" analysis, China's total military expenditure is likely to exceed that of the US by about 2025. This in a region, Asia, filled with every kind of strategic challenge – from the divided Korean peninsula through the disputed Taiwan straits to the standoff between nuclear-armed India and Pakistan. Unlike for the last half-century, US hegemony can no longer be relied on to keep the peace. To craft a new Pax Pacifica is therefore the great strategic challenge of our time. Australia, as "a western country in Asia", would do what it could.

In response to the Zhang-McCain exchange, Rudd calmly sketched both the huge growth in individual freedom and prosperity in China over the past 30 years, and the distance still to go before China can be described as a well-governed country under the rule of law. Implicitly rejecting the positions taken by both McCain and Zhang, he said "we need to shape global values together".

That seems to me exactly right. Both the US and China must be prepared to get into a conversation about the terms of international order in the 21st century. Each country must remain true to its own values, but work to see where there is common ground – and where adjustment, compromise or simply agreeing to disagree are viable.

This may fail, but it would be criminal folly not to attempt it. So Xi and Barack Obama should now plan to take a joint summer retreat on the coast of Australia, guided by Rudd, with a snorkelling trip to the Great Barrier Reef. Full-blown, Castlemaine XXXX mateship between Chinese and Americans may be too much to expect, but it is essential for them to open a frank, strategic conversation about global values and the foundations of international order.